|By Paola Arosio and Silvia Aloisi

MILAN (Reuters) - Fabrizio Viola, the chief executive of troubled Italian bank Monte dei Paschi di Siena, has agreed to quit and allow a new boss to try to convince reluctant investors to back an emergency rescue plan.

The Tuscan lender, which emerged as Europe's weakest bank in stress tests in July, said on Thursday it was working to appoint a successor quickly and that Viola would remain in place until that was done.

Marco Morelli, the head of Bank of America Merrill Lynch in Italy, was almost certain to take Viola's job, a source with knowledge of the matter said.

"It'll be him at 99.9 percent," the source said, adding the decision to replace Viola was because the bank needed "a change of gear" to persuade investors to buy into a capital increase of up to 5 billion euros ($5.6 billion) -- one of the main pillars of its bailout plan.

Another senior source said the bank had "basically" identified a successor for Viola, refusing to give more details.

A person close to Morelli, who was Monte dei Paschi's chief financial officer until 2010, said he had not been contacted for the time being.

A third source said Corrado Passera, who has served as industry minister and headed bank Intesa Sanpaolo, could also be a candidate for the job.

Passera, backed by investment bank UBS, presented a last-ditch rival bailout plan for Monte dei Paschi in July but was rebuffed by the bank's board.

CASH CALL DELAYED?

Time is tight as the lender has committed to launch the capital increase -- its third in as many years -- before the end of the year as part of the privately-funded rescue blueprint agreed with the European Central Bank.

However, one of the sources said the fund raising was now more likely to be launched in January or February of 2017, a delay that should allow Italy's political situation to become clearer.

The health of the country's third-largest lender poses a threat to the wider banking system, the savings of thousands of small investors and also to the weakening political authority of Prime Minister Matteo Renzi, who faces a make-or-break constitutional referendum this autumn.

A source at Italy's Treasury, which is the top shareholder in Monte dei Paschi with a 4 percent stake, said the situation was under control and a new CEO would be appointed soon.

The bank gave no reason for the departure of Viola, who took charge of Monte dei Paschi in 2012 just as the lender was on the brink of collapse because of the euro zone debt crisis.

Several bankers had said it would be difficult for Viola, who has already tapped the market for cash in 2014 and 2015, to lead another fundraising.

POLITICAL UNCERTAINTY

Further complicating the picture is the constitutional referendum on which Renzi has staked his job, expected to be held in late November or early December.

According to a banker close to the situation investors want to see the outcome of the vote before deciding whether to buy into Monte dei Paschi's capital increase. A defeat for Renzi would increase political uncertainty and dampen sentiment towards Italian assets.

With larger Italian bank UniCredit also expected to launch a multi-billion euro capital increase in coming months, the two banks could find themselves courting investors at the same time.

Wary of the risks, JP Morgan and Mediobanca, global coordinators for the Monte dei Paschi's cash call, are working on a possible conversion of the bank's subordinated bonds into shares to reduce to size of the capital increase by around 2 billion euros, sources have said. ($1 = 0.8889 euros)

(additional reporting by Silvia Ognibene in Siena and Stefano Bernabei in Rome; Editing by Keith Weir)